2014/01/15 by Maciej Gawron, Gawron, Maciej · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT
paper · pdf · doi:10.48550/arxiv.1401.3553
9 pages, submitted
arxiv created 2014/01/15 · arxiv updated 2014/01/16
We investigate the Stern polynomials defined by B0 ( t ) =0,B1 ( t ) =1, and for n ≥ 2 by the recurrence relations B2n( t) =tBn( t) , B2n+1( t) =Bn( t) +Bn+1( t) . We prove that all possible rational roots of that polynomials are 0,-1,-1/2,-1/3. We give complete characterization of n such that deg( Bn) = deg( Bn+1) and deg( Bn) =deg( Bn+1) =deg( Bn+2) . Moreover, we present some result concerning reciprocal Stern polynomials.